113
edits
Fundamental Theorem of Calculus: Difference between revisions
→Physical intuition
| Line 16: | Line 16: | ||
In the case of a particle traveling in a straight line, its position, ''x'', is given by ''x''(''t'') where ''t'' is time and ''x''(''t'') means that ''x'' is a function of ''t''. The derivative of this function is equal to the infinitesimal change in quantity, d''x'', per infinitesimal change in time, d''t'' (of course, the derivative itself is dependent on time). This change in displacement per change in time is the velocity ''v'' of the particle. In Leibniz notation: | In the case of a particle traveling in a straight line, its position, ''x'', is given by ''x''(''t'') where ''t'' is time and ''x''(''t'') means that ''x'' is a function of ''t''. The derivative of this function is equal to the infinitesimal change in quantity, d''x'', per infinitesimal change in time, d''t'' (of course, the derivative itself is dependent on time). This change in displacement per change in time is the velocity ''v'' of the particle. In Leibniz notation: | ||
<math>\frac{dx}{dt} | <math>\frac{dx}{dt}</math> | ||
Rearranging this equation, it follows that: | Rearranging this equation, it follows that: | ||